/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 You are sick, and your temperatu... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

You are sick, and your temperature is 312.0 kelvins. Convert this temperature to the Fahrenheit scale.

Short Answer

Expert verified
312.0 K is 101.93°F in the Fahrenheit scale.

Step by step solution

01

Understand the Conversion Formula

To convert a temperature from Kelvin to Fahrenheit, you can use the formula: \( F = \frac{9}{5}(K - 273.15) + 32 \), where \( F \) is the temperature in Fahrenheit, and \( K \) is the temperature in Kelvin.
02

Subtract 273.15 from Kelvin

First, subtract 273.15 from the given temperature in Kelvins: \[ 312.0 - 273.15 = 38.85 \]. This gives you the equivalent temperature in Celsius.
03

Apply the Conversion Formula

Now, substitute the Celsius value into the conversion equation: \[ F = \frac{9}{5} \times 38.85 + 32 \].
04

Calculate the Multiplication and Addition

First, calculate the multiplication: \( \frac{9}{5} \times 38.85 = 69.93 \). Then add 32: \[ 69.93 + 32 = 101.93 \].
05

State the Fahrenheit Temperature

The temperature in Fahrenheit is now found to be 101.93°F.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Kelvin to Fahrenheit conversion
Converting temperatures between different scales is a common task in physics and daily life. To convert from Kelvin to Fahrenheit, we use a specific mathematical formula. The formula is:\[F = \frac{9}{5}(K - 273.15) + 32\]Here, \(F\) represents the temperature in Fahrenheit, while \(K\) stands for the temperature in Kelvin. This formula is derived from the direct relationship between Celsius and Fahrenheit, adjusted for the absolute temperature scale.

Steps to convert:
  • First, convert the temperature from Kelvin to Celsius by subtracting 273.15.
  • Then, apply the conversion formula to switch from Celsius to Fahrenheit.
  • Finally, perform the arithmetic operations to get the temperature in Fahrenheit.
This way, a temperature of 312.0 Kelvin becomes 101.93°F.
temperature scales
Temperature scales are systems used to measure thermal energy levels. They help determine how hot or cold an object is. The most common temperature scales are Kelvin, Celsius, and Fahrenheit.

- **Kelvin**: A scientific scale that starts at absolute zero, the point where particles theoretically stop moving. It's mainly used in scientific research. - **Celsius**: This is a popular scale in most of the world for weather forecasts and general temperature measurement. It starts at the freezing point of water (0°C) and boils at 100°C under standard conditions. - **Fahrenheit**: Predominantly used in the United States for non-scientific purposes. Water freezes at 32°F and boils at 212°F.
Each scale serves different purposes, with Kelvin being particularly crucial in physics and thermodynamics to describe thermal energy objectively.
unit conversion in physics
Unit conversion is an essential skill in physics to ensure measurements are communicated accurately across different systems. This process involves converting from one unit of measurement to another without altering the inherent quantity.

In temperature conversion, understanding the relationship between different scales is crucial. Make sure to:
  • Understand the mathematical relations between the units.
  • Apply consistent and accurate conversion formulas.
  • Perform calculations step by step to avoid errors.
For example, when converting a known temperature from Kelvin to Fahrenheit, you need to subtract a constant to switch to Celsius first, then use the proportionality factor between Celsius and Fahrenheit. Such skills are foundational not only in physics but also in engineering, chemistry, and everyday applications, ensuring clarity and precision.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Ideally, when a thermometer is used to measure the temperature of an object, the temperature of the object itself should not change. However, if a significant amount of heat flows from the object to the thermometer, the temperature will change. A thermometer has a mass of \(31.0 \mathrm{g}\), a specific heatcapacity of \(c=815 \mathrm{J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right),\) and a temperature of \(12.0^{\circ} \mathrm{C} .\) It is immersed in \(119 \mathrm{g}\) of water, and the final temperature of the water and thermometer is \(41.5^{\circ} \mathrm{C} .\) What was the temperature of the water before the insertion of the thermometer?

You and your team are given the task of constructing a crude thermometer that covers a temperature range from \(0^{\circ} \mathrm{C}\) to \(60^{\circ} \mathrm{C} .\) You have at your disposal an aluminum rod of length \(L_{0}=2.00 \mathrm{m}\) (at \(\left.T=0^{\circ} \mathrm{C}\right)\) and diameter \(D=0.50 \mathrm{cm},\) and a broken clock that is missing its hour hand, and its longer minute hand is hanging loose and pointing in the six o"clock direction. The long hand of the clock is 8.20 inches long and pivots loosely at the clock's center. You get the idea to mount the rod horizontally so that one end butts against a wall and the other end pushes against the dangling minute hand of the clock. A temperature-induced change in the length of the rod will then be reflected in a change in the angle that the minute hand makes with the vertical (i.e., relative to the six o'clock position). (a) If you want the full temperature range to span the angle between the 6 and 7 markings (uniformly spaced) on the clock, how far from the central pivot should the end of the rod make contact with the minute hand? (b) The current temperature in the room is \(65.0^{\circ} \mathrm{F} .\) At what angle relative to the vertical (the six o'clock position) should the minute hand point at this temperature if it is to point directly at 6 when \(T=0^{\circ} \mathrm{C} ?\) (c) What would be the angular range of your "clock-thermometer" if the rod were made of steel, rather than aluminum? Assume that it is placed at the same position on the minute hand as determined in (a).

Blood can carry excess energy from the interior to the surface of the body, where the energy is dispersed in a number of ways. While a person is exercising, \(0.6 \mathrm{kg}\) of blood flows to the body's surface and releases \(2000 \mathrm{J}\) of energy. The blood arriving at the surface has the temperature of the body's interior, \(37.0^{\circ} \mathrm{C} .\) Assuming that blood has the same specific heat capacity as water, determine the temperature of the blood that leaves the surface and returns to the interior.

A 42 -kg block of ice at \(0^{\circ} \mathrm{C}\) is sliding on a horizontal surface. The initial speed of the ice is \(7.3 \mathrm{m} / \mathrm{s}\) and the final speed is \(3.5 \mathrm{m} / \mathrm{s} .\) Assume that the part of the block that melts has a very small mass and that all the heat generated by kinetic friction goes into the block of ice. Determine the mass of ice that melts into water at \(0^{\circ} \mathrm{C}\).

The vapor pressure of water at \(10^{\circ} \mathrm{C}\) is \(1300 \mathrm{Pa}\). (a) What percentage of atmospheric pressure is this? Take atmospheric pressure to be \(1.013 \times 10^{5}\) Pa. (b) What percentage of the total air pressure at \(10^{\circ} \mathrm{C}\) is due to water vapor when the relative humidity is \(100 \% ?\) (c) The vapor pressure of water at \(35^{\circ} \mathrm{C}\) is 5500 Pa. What is the relative humidity at this temperature if the partial pressure of water in the air has not changed from what it was at \(10^{\circ} \mathrm{C}\) when the relative humidity was \(100 \% ?\)

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.